Gary McCartor

Regional Seismic-Event Characterization Using a Bayesian Formulation of Simple Kriging

An approach is presented to calibrate and use regional P - S amplitude ratios to improve seismic-event characterization capabilities with regard to monitoring the Comprehensive Nuclear-Test-Ban Treaty. Data for presumed earthquakes are used to estimate distance corrections for Pn - Sn and Pn - Lg ratios in the 6–8-Hz pass-band for tectonic and stable-region types. The regional phase-amplitude ratios are further corrected for path variations using simple kriging. Simple kriging is derived using a Bayesian approach. A correction surface is determined for each type of amplitude ratio at each station as an optimal linear combination of existing amplitude-ratio data at the station, giving greater weight to calibration data nearer to the correction location. A corresponding uncertainty surface is also estimated in terms of the residual variance of the data and a calibration variance. For well-calibrated locations, the correction converges to the mean of nearby data, and the uncertainty converges to the residual variance. For locations far from calibration data, the correction surface converges to the worldwide average, with larger uncertainty. With these correction and uncertainty surfaces, corrected values of Pn / Smax (6–8 Hz) are obtained and used to define a hypothesis test that fixes the significance level with respect to misclassifying explosions. The criterion is applied to 140 explosions at known nuclear-test sites and to 4173 Reviewed Event Bulletin (REB) events above mb 3.5 (presumed to be mostly earthquakes) with regional recordings between 3° and 17°, Pn signal-to-noise ratio (SNR) >2.0, and Sn or Lg SNR >1.3. At a 0.005 significance level, none of the 140 explosions at any of the known nuclear-test sites are screened out, whereas about 78% of the REB events are screened out. Correcting regional P - S ratios for spatial variations improves the screening performance by about 25% over just correcting for distance. The screening results are fairly insensitive to estimates of parameters (correlation length, calibration variance, and residual variance) that are used, along with data, to compute the correction and uncertainty surfaces at each station.

Pauli-Villars as a Nonperturbative Ultraviolet Regulator in Discretized Light-Cone Quantization

We propose a solution to the problem of renormalizing light-cone Hamiltonian theories while maintaining Lorentz invariance and other symmetries. The method uses generalized Pauli–Villars regulators to render the theory finite. We discuss the method in the context of Yukawa theory at one loop and for a soluble model in 3+1 dimensions. The model is studied nonperturbatively. Numerical results obtained with use of discretized light-cone quantization, special integration weighting factors, and the complex symmetric Lanczos diagonalization algorithm compare well with the analytic answers.

Application of Pauli--Villars Regularization and Discretized Light-Cone Quantization to a Single-Fermion Truncation of Yukawa Theory

We apply Pauli{Villars regularization and discrete light-cone quantization to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a singlefermion truncation. Three heavy scalars, including two with negative norm, are used to regulate the theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of a new, indenite-metric Lanczos algorithm. Various observables are extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope.

The mass renormalization of nonperturbative light-front Hamiltonian theory: an illustration using truncated, Pauli–Villars-regulated Yukawa interactions

Abstract We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli–Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. The limit of infinite Pauli–Villars mass receives special scrutiny.

Exact Solutions to Pauli–Villars-Regulated Field Theories

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli–Villars fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, we also discuss how perturbation theory in the difference between the masses of the physical and Pauli–Villars particles could be developed, thus generating physical theories. The existence of explicit solutions of the solvable theory also allows one to study the relationship between the equal-time and light-cone vacua and eigensolutions. 12.38.Lg, 11.15.Tk, 11.10.Gh, 11.10.Ef

Bosonic zero modes in discretized light-cone field theory

It is shown that for theories with bosonic fields a constrained zero mode is a necessary ingredient for a consistent discretized light-cone quantization (DLCQ). Inclusion of this zero mode is shown to remove a non-covariant, quadratically divergent contribution to the fermion self-energy in 3+1 dimensional Yukawa theory which would otherwise be present. It is further shown to result in a fully consistent set of Heisenberg equations. The possibility of maintaining parity in DLCQ is discussed.

Schwinger model in the light-cone representation

I present a solution to the Schwinger model in the light-cone representation which corrects an error in a previous work. I emphasize the details of the mechanism by which the physical vacuum is different than the perturbative vacuum. I suggest that the method of analyzing vacuum structure presented here may be of use in more complicated theories such as QCD.

Two-boson truncation of Pauli-Villars-regulated Yukawa theory

We apply light-front quantization, Pauli-Villars regularization, and numerical techniques to the nonperturbative solution of the dressed-fermion problem in Yukawa theory in 3 + 1 dimensions. The solution is developed as a Fock-state expansion truncated to include at most one fermion and two bosons. The basis includes a negative-metric heavy boson and a negative-metric heavy fermion in order to provide the necessary cancellations of ultraviolet divergences. The integral equations for the Fock-state wave functions are solved by reducing them to effective one-boson--one-fermion equations for eigenstates with J{sub z} = 1/2. The equations are converted to a matrix equation with a specially tuned quadrature scheme, and the lowest mass state is obtained by diagonalization. Various properties of the dressed-fermion state are then computed from the nonperturbative light-front wave functions. This work is a major step in our development of Pauli-Villars regularization for the nonperturbative solution of four-dimensional field theories and represents a significant advance in the numerical accuracy of such solutions.

Light-cone gauge Schwinger model

Nakawakis Coulomb gauge solution to the Schwinger model is transformed to light-cone gauge. Various options for maintaining the gauge invariance necessary to satisfy the equations of motion are discussed. Satisfactory light-cone gauge solutions are found and are used to study light-cone quantization, the calculation of the dynamical operators and properties of the vacua in the light-cone representation. The solutions found here can be used to justify previous light-cone Tamm-Dancoff calculations performed by others.

Light-cone quantization of gauge fields

Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the “discretized” light-cone quantization of gauge fields are discussed.